TY - JOUR
AU - Ozdemir, Hilal Basak
AU - Keskin, Refik
PY - 2015/07/28
Y2 - 2021/09/19
TI - A Note on Some Diophantine Equations
JF - MATEMATIKA: Malaysian Journal of Industrial and Applied Mathematics
JA - MATEMATIKA: MJIAM
VL - 31
IS - 1
SE - Articles
DO - 10.11113/matematika.v31.n1.745
UR - https://matematika.utm.my/index.php/matematika/article/view/745
SP - 59-61
AB - In this study, we solve the equations (x+y+1)²=5xy, (x+y-1)²=5xy, and (x-y+1)²=5xy. We find all positive integer solutions of these equations in terms of Fibonacci and Lucas sequences. By using the solutions of these equations we give all positive integer solutions of the equations x²+y²-3xy+x=0, x²+y²-3xy-x=0, and x²+y²-7xy-x=0. Moreover, it is shown that the equation x²+y²-7xy+x=0 has no positive integer solutions.
ER -